That means the foci are at and
2. A hyperbola is defined by a constant difference of the distances between a point L on the hyperbola and the foci:
3. The excentricity of a hyperbola is calculated by:
Since the excentricity is e = 5 you can determine the value of b.
(For this part I used my computer)
4. Therefore the equation of the hyperbola is:
5. I've attached a drawing of the ellipse and the hyperbola with the point L on the right branch.